Properties

Label 73.44
Level $73$
Weight $0$
Character 73.1
Symmetry odd
\(R\) 2.886357
Fricke sign not computed rigorously

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Maass form invariants

Level: \( 73 \)
Weight: \( 0 \)
Character: 73.1
Symmetry: odd
Fricke sign: not computed rigorously
Spectral parameter: \(2.8863571294675357507760458289 \pm 2 \cdot 10^{-4}\)

Maass form coefficients

The coefficients here are shown to at most $8$ digits of precision. Full precision coefficients are available in the downloads.

\(a_{1}= +1 \) \(a_{2}= -1.75019926 \pm 9.4 \cdot 10^{-1} \) \(a_{3}= +0.65822284 \pm 8.8 \cdot 10^{-1} \)
\(a_{4}= +2.06319745 \pm 9.8 \cdot 10^{-1} \) \(a_{5}= -1.37759468 \pm 8.5 \cdot 10^{-1} \) \(a_{6}= -1.15202113 \pm 1.0 \)
\(a_{7}= -0.88382310 \pm 8.2 \cdot 10^{-1} \) \(a_{8}= -1.86080738 \pm 9.4 \cdot 10^{-1} \) \(a_{9}= -0.56674269 \pm 8.7 \cdot 10^{-1} \)
\(a_{10}= +2.41106520 \pm 1.0 \) \(a_{11}= +0.24496749 \pm 7.6 \cdot 10^{-1} \) \(a_{12}= +1.35804368 \pm 1.0 \)
\(a_{13}= +1.07672655 \pm 7.8 \cdot 10^{-1} \) \(a_{14}= +1.54686653 \pm 1.0 \) \(a_{15}= -0.90676429 \pm 9.7 \cdot 10^{-1} \)
\(a_{16}= +1.19358625 \pm 9.1 \cdot 10^{-1} \) \(a_{17}= -0.57702241 \pm 7.4 \cdot 10^{-1} \) \(a_{18}= +0.99191264 \pm 1.0 \)
\(a_{19}= +1.24968216 \pm 7.7 \cdot 10^{-1} \) \(a_{20}= -2.84224983 \pm 1.1 \) \(a_{21}= -0.58175255 \pm 8.9 \cdot 10^{-1} \)
\(a_{22}= -0.42874192 \pm 9.6 \cdot 10^{-1} \) \(a_{23}= +1.53808909 \pm 7.0 \cdot 10^{-1} \) \(a_{24}= -1.22482592 \pm 9.7 \cdot 10^{-1} \)
\(a_{25}= +0.89776711 \pm 7.9 \cdot 10^{-1} \) \(a_{26}= -1.88448600 \pm 9.4 \cdot 10^{-1} \) \(a_{27}= -1.03126583 \pm 8.7 \cdot 10^{-1} \)
\(a_{28}= -1.82350155 \pm 1.0 \) \(a_{29}= -0.55902603 \pm 7.7 \cdot 10^{-1} \) \(a_{30}= +1.58701818 \pm 1.1 \)
\(a_{31}= +1.48146676 \pm 7.5 \cdot 10^{-1} \) \(a_{32}= -0.22820638 \pm 9.1 \cdot 10^{-1} \) \(a_{33}= +0.16124320 \pm 8.2 \cdot 10^{-1} \)
\(a_{34}= +1.00990420 \pm 9.4 \cdot 10^{-1} \) \(a_{35}= +1.21755000 \pm 9.0 \cdot 10^{-1} \) \(a_{36}= -1.16930207 \pm 1.0 \)
\(a_{37}= +1.04399816 \pm 7.8 \cdot 10^{-1} \) \(a_{38}= -2.18719280 \pm 9.7 \cdot 10^{-1} \) \(a_{39}= +0.70872601 \pm 9.0 \cdot 10^{-1} \)
\(a_{40}= +2.56343835 \pm 9.4 \cdot 10^{-1} \) \(a_{41}= -1.49218998 \pm 7.4 \cdot 10^{-1} \) \(a_{42}= +1.01818288 \pm 1.0 \)
\(a_{43}= +0.59930476 \pm 8.0 \cdot 10^{-1} \) \(a_{44}= +0.50541630 \pm 9.9 \cdot 10^{-1} \) \(a_{45}= +0.78074172 \pm 9.7 \cdot 10^{-1} \)
\(a_{46}= -2.69196239 \pm 7.7 \cdot 10^{-1} \) \(a_{47}= -0.33634019 \pm 7.1 \cdot 10^{-1} \) \(a_{48}= +0.78564573 \pm 8.9 \cdot 10^{-1} \)
\(a_{49}= -0.21885673 \pm 7.9 \cdot 10^{-1} \) \(a_{50}= -1.57127133 \pm 9.3 \cdot 10^{-1} \) \(a_{51}= -0.37980933 \pm 7.9 \cdot 10^{-1} \)
\(a_{52}= +2.22149946 \pm 9.5 \cdot 10^{-1} \) \(a_{53}= -0.90092581 \pm 7.8 \cdot 10^{-1} \) \(a_{54}= +1.80492069 \pm 1.1 \)
\(a_{55}= -0.33746592 \pm 8.0 \cdot 10^{-1} \) \(a_{56}= +1.64462454 \pm 9.9 \cdot 10^{-1} \) \(a_{57}= +0.82256935 \pm 8.4 \cdot 10^{-1} \)
\(a_{58}= +0.97840694 \pm 8.7 \cdot 10^{-1} \) \(a_{59}= +1.40628799 \pm 7.4 \cdot 10^{-1} \) \(a_{60}= -1.87083376 \pm 1.1 \)

Displaying $a_n$ with $n$ up to: 60 180 1000